Receiver for alamouti type space-time block coding FBMC system

ABSTRACT

A method of reception of signals transmitted by a FBMC transmitter using a block Alamouti coding. After demodulation in a base band, the received signal is sampled, with the sample blocks undergoing a sliding FFT before being de-multiplexed towards a first path during a first use of the channel and a second path during a second use of the channel. The vectors received on the first path are multiplied by a first and a second transfer matrix, conjugated to provide first and second vectors. The vectors received on a second path undergo time-reversal and complex conjugation and, if appropriate, multiplication by an imaginary factor, depending on the size of the blocks. The vectors thus obtained are multiplied by first and second transfer matrices to provide third and fourth vectors. The first and fourth (second and third vectors) are then combined and the combined vector is filtered and spectrally de-spread to give an estimate of the block transmitted by the first (second) antenna of the transmitter during the first use of the channel.

TECHNICAL FIELD

The present invention relates in general to the field oftelecommunications systems that use a filter bank multi-carrier (FBMC)modulation system. It also relates to MISO (Multiple Input SingleOutput) or even MIMO (Multiple Input Multiple Output) telecommunicationsystems that use space-time coding.

STATE OF THE PRIOR ART

Telecommunication systems which use multi-carrier modulation are wellknown in the state of the art. The principle for such modulationinvolves dividing the transmission band into a plurality of frequencysub-channels associated with sub-carriers and modulating each of thesesub-carriers using the data to be transmitted.

The most widely used multi-carrier modulation is without doubtOrthogonal Frequency Division Multiplexing (OFDM) modulation. However,since the spectral occupation of an OFDM signal is substantially greaterthan the band of sub-carriers that it uses because of the spreading ofthe secondary lobes, OFDM modulation is not an optimum solution forapplications that require high levels of out-of-band rejection.

Modulation using banks of filters or Filter Bank Multi-Carriermodulation (FBMC) is multi-carrier modulation that provides betterspectral localisation within the band of sub-carriers. It is moreoverone of the possible solutions for fifth generation telecommunicationsystems.

The principle of FBMC modulation is based on synthesis using a filterbank on transmission and analysis using a filter bank on reception,where the product of the transfer function of a filter at transmissionand the transfer function of the corresponding filter at reception isequal to the transfer function of the Nyquist filter.

FBMC systems are conventionally implemented in the time domain. Thestructure of an FBMC system implemented in the time domain has beendescribed in detail in the article by Hirosaki entitled “An orthogonallymultiplexed QAM system using the discrete Fourier transform” publishedin IEEE Trans on Comm., vol. 29 No. 7, pp. 982-989, July 1981, as wellas in the article by P. Siohan et al. entitled “Analysis and design ofOFDM/OQAM systems based on filterbank theory” published in IEEE Trans.on signal processing, vol. 50, No 5, pp. 1170-1183, May 2002. FBMCsystems implemented in the time domain make use of networks of polyphasefilters, hence their denomination of PPN-FBMC (Polyphase Network FBMC).

More recently the implementation of an FBMC system in the frequencydomain has been proposed as described in the document by M. Bellanger etal. entitled “FBMC physical layer: a primer” available at the websitewww.ict-phydyas.org. FBMC systems implemented in the frequency domainmake use of spectral spread, hence their denomination of FS-FBMC(Frequency Spread FBMC).

The structure of an FS-FBMC system is shown in FIG. 1.

At the transmitter, the QAM modulation symbols to be transmitted at arate Nf where f=1/T are grouped together in blocks of size N, x₀[n], . .. , x_(N-1)[n] where n is the time index of the block. Each block of Nsymbols is supplied in parallel to N input paths of a pre-processingmodule, 110, called Offset QAM pre-processing (OQAM). The function ofthis pre-processing module is to demultiplex the real portion andimaginary portion of the input signals with a frequency 2f, so that oftwo samples transmitted at the same instant over two successivesub-channels or two samples transmitted at two successive instants overthe same channel, one is real and one is imaginary. Each of the N outputpaths from the pre-processing module 110 corresponds to a sub-channel.

Each sub-channel is then spread over an interval of 2K−1 adjacentsub-carriers, centered on a central sub-carrier of the sub-channel. Morespecifically, each item of OQAM data is spread over 2K−1 adjacentsub-carriers and weighted by the (real) value taken by the synthesisfilter transfer function at the corresponding frequency.

Reference 120 designates the module for frequency spread and filteringby the prototype filter. Each item of OQAM data d_(i) [n] at the inputto the module 120 is spread over 2K−1 adjacent sub-carriers to give:{hacek over (d)} _(i,k) [n]=d _(i) [n]G _(k) ,k=−K+1, . . . ,0, . . .,K−1  (1)Data with the same parity i and i+2 are spectrally separated and datawith opposite parities i and i+1 overlap as shown in FIG. 2A. Thisoverlap does not however result in any interference, since two items ofdata with opposite parities are necessarily located on the real axis andon the imaginary axis and are separated by T/2. For example, in FIG. 2A,the data d_(i) [n] and d_(i+2)[n] are real values (shown as continuouslines) whereas the data item d_(i+1) [n] is an imaginary value(represented by broken lines). The imaginary values are presented to theinput to the IFFT module with an offset of T/2 relative to the realvalues. Orthogonality in the complex plane is preserved by the filteringby the prototype filter, given that the coefficients G_(k) are real.

The data spread over frequency and filtered then undergoes an IFFT ofsize KN in 130.

The block of temporal sample at the output of the IFFT is combined usingthe combination module 140 as indicated in FIG. 3. All of the samples atthe output of the IFFT represent an FBMC symbol in the time domain, withtwo successive FBMC symbols being offset by T/2 (in other words N/2samples) and each of the FBMC symbols having a duration KT (in otherwords a size of KN samples). An FBMC symbol is combined in module 140with the K−1 preceding FBMC symbols and K−1 following FBMC symbols. Forthis reason K is also called the overlapping factor or interlacingfactor. It can be seen that a sample at the output of the combinationmodule 140 is the sum of 2K−1 consecutive samples of FBMC symbols.

The signal thus obtained is then translated to a carrier frequency.

After transmission on the channel 150, the received signal, base banddemodulated, is sampled by the receiver at a rate Nf then converted intoblocks of size KN by the serial-parallel converter 160.

A sliding FFT (the window of the sliding FFT for N/2 samples between twoFFT calculations) of size KN is carried out in the FFT module 170 onblocks of KN consecutive samples at the output from the serial-parallelconverter 160.

The outputs from the FFT then undergo filtering and spectralde-spreading in module 180. The de-spreading operation takes place inthe frequency domain as shown in FIG. 2B. More specifically, the samples{hacek over (d)}_(i,k) ^(r) [n], k=−K+1, . . . , 0, . . . , K−1 whichcorrespond to the 2K−1 frequencies (i−1)K+1, . . . iK, . . . (i+1)K−1 ofthe FFT are multiplied by the values of the transfer function of theanalysis filter (translated in frequency from that of the prototypefilter) at the frequencies in question and the results obtained aresummed, that is:

$\begin{matrix}{{d_{i}^{r}\lbrack n\rbrack} = {\sum\limits_{k = {{- K} + 1}}^{K - 1}\;{G_{k}{{\overset{\Cup}{d}}_{i,k}^{r}\lbrack n\rbrack}}}} & (2)\end{matrix}$

It can be seen that as in FIG. 2A, obtaining data which has ranks of thesame parity, for example d_(i) ^(r) [n] and d_(i+2) ^(r) [n], makes useof disjoint sample blocks whereas those of two consecutive ranks, withinverse parities, overlap. Thus obtaining the data item d_(i+1) ^(r) [n]makes use of samples {hacek over (d)}_(i,k) ^(r) [n], k=1, . . . , K−1as well as of samples {hacek over (d)}_(i+2,k) ^(r) [n], k=−K+1, . . . ,1.

The de-spreading of real data is represented by continuous lines whereasthat for imaginary data is represented by dotted lines.

The data d_(i) ^(r) [n] thus obtained are then supplied apost-processing module 190 which carries out the reverse processing ofthat of module 110, in other words OQAM demodulation. The QAM symbolsare thus restored.

FBMC technology is one of the candidate technologies for fifthgeneration wireless telecommunication systems. In particular the lattermust allow the requirements of spectral fragmentation and transmissionasynchronism of MTC (Machine Type Communication) communications to bemet.

The application of FBMC technology to MIMO (Multiple Input MultipleOutput) spatial diversity type telecommunication systems is however muchmore complicated than in OFDM because FBMC transmission intrinsicallyuses orthogonality in the complex plane to eliminate interferencebetween FBMC symbols.

Spatial Time Block Coding, or STBC, of the Alamouti type has recentlybeen proposed for a FBMC system in the article by M. Renfors et al.entitled “A block-Alamouti scheme for filter bank based multicarriertransmission” published in Proceedings of European Wireless ConferenceEW 2010, Apr. 12-15, 2010, Lucca, Italy. 2010. pp. 1031-1037.

It should first of all be recalled that Alamouti coding is STBC (SpaceTime Block Coding) which is applied to a configuration with twotransmission antennas and one reception antenna. Its coding matrix isgiven by:

$\begin{matrix}{C = \begin{pmatrix}x_{0} & x_{1} \\{- x_{1}^{*}} & x_{0}^{*}\end{pmatrix}} & (3)\end{matrix}$wherein x₀ and x₁ are two complex symbols (belonging to a modulationalphabet) to be transmitted. During a first use of the channel (that is,a first transmission interval) the transmission antennas respectivelytransmit x₀ and x₁, and during a second use of the channel theseantennas transmit −x₁*and x₀*.

The signals received, respectively, during the first and second use ofthe channel, y₀, y₁ may then be expressed in the following form:y ₀ =h ₀ x ₀ +h ₁ x ₁ +n ₀  (4-1)y ₁ =−h ₀ x ₁ *+h ₁ x ₀ *+n ₁  (4-2)where h₀,h₁ are, respectively, the complex coefficient of the firstelementary channel between the first transmission antenna and thereception antenna, and the complex coefficient of the second elementarychannel between the second transmission antenna and the receptionantenna, and where n₀,n₁ are noise samples, assumed to be additive andindependent, from a given centred white Gaussian process.

Assuming that the channel is known, the receiver estimates thetransmitted symbols from a combination of the received signals:

$\begin{matrix}{{\hat{x}}_{0} = {{\frac{1}{| h_{0} \middle| {}_{2}{+ | h_{1} |^{2}} }( {{h_{0}^{*}y_{0}} + {h_{1}y_{1}^{*}}} )} = {x_{0} + \frac{{h_{0}^{*}n_{0}} + {h_{1}n_{1}^{*}}}{| h_{0} \middle| {}_{2}{+ | h_{1} |^{2}} }}}} & ( {5\text{-}1} ) \\{{\hat{x}}_{1} = {{\frac{1}{| h_{0} \middle| {}_{2}{- | h_{1} |^{2}} }( {{h_{1}^{*}y_{0}} + {h_{0}y_{1}^{*}}} )} = {x_{1} + \frac{{h_{1}^{*}n_{0}} - {h_{0}n_{1}^{*}}}{| h_{0} \middle| {}_{2}{+ | h_{1} |^{2}} }}}} & ( {5\text{-}2} )\end{matrix}$

The aforementioned article by Renfors makes use of an appropriatefiltering technique, already used for Alamouti coding in the presence ofintersymbol interference, described in the article by E. Lindskog et al.entitled “A transmit scheme for channels with intersymbol interference”published in Proc. IEEE of Int'l Conf. on Communications, ICC 2000, pp.307-311, June 2000.

The Alamouti coding is carried out using blocks of input data vectors, ablock being made up of a sequence of L column vectors, and which maytherefore be represented by a matrix X of size N×L where N is the numberof sub-carriers. Each column vector of the matrix X, that is X^(m), m=0,. . . , L−1, here represents a vector of complex signals at the outputof the OQAM modulator. It will be recalled that because of OQAMmodulation, of any two adjacent elements (along lines or in columns) ofthe matrix X, one is real and the other imaginary.

If two successive blocks are referred to as X ₀ and X ₁, the Alamoutiblock coding matrix, as proposed in the article by Renfors, can beexpressed in the following form:

$\begin{matrix}{\overset{\_}{C} = \begin{pmatrix}{\overset{\_}{X}}_{0} & {\overset{\_}{X}}_{1} \\{{- {\overset{\_}{X}}_{1}^{*}}T} & {{\overset{\_}{X}}_{0}^{*}T}\end{pmatrix}} & (6)\end{matrix}$The block-columns of the block-matrix here represent the antennae andthe block-lines represent the uses of the channel. In each of theblocks, the lines represent the sub-carriers and the columns representthe time. T is an anti-diagonal matrix of size L×L all of whoseanti-diagonal elements are equal to 1, and thus translates a timereversal. Thus, if X is a sequence of vectors X⁰, X¹, . . . , X^(L−1)the block XT is made up of the sequence X^(L−1), X^(L−2), . . . , X⁰.

La FIG. 4 schematically shows a sequence of blocks of symbolstransmitted by an FBMC transmitter using block Alamouti coding.

A first sequence of blocks 401 is formed by a first guard block 411, afirst block of L symbol vectors, X ₀, 421, a second guard block, 431, afirst transformed block, −X ₁*T, 441, made up of L symbol vectors,followed by a third guard block 451.

A second sequence of blocks 402 is formed by a first guard block 421, asecond block made up of L symbol vectors, X ₁, 422, a second guardblock, 432, a second transformed block, X ₀*T, 442, made up of L symbolvectors, followed by a third guard block, 452.

The guard blocks are made up of null symbols, and their purpose is toisolate successive blocks from interference generated by adjacentblocks.

The first sequence of blocks is transmitted by the first antenna 491after FBMC modulation. The signal obtained at the output from the FBMCmodulator may be regarded as a sequence of FBMC symbols overlapping intime, as explained in relation to FIG. 3. The signal thus obtained istransmitted on the first antenna, after having been translated to an RFband.

Similarly, the second sequence of blocks is transmitted by the secondantenna 492 after having been modulated by a second FBMC modulator withan identical structure to the first.

FIG. 5 schematically shows the architecture of an FBMC receiver used toreceive sequences of blocks of symbols transmitted by the transmitter inFIG. 4. It is essential to note that this FBMC receiver exhibitsconventional architecture (time-based implementation) and not FS-FBMCarchitecture (frequency-based implementation).

The receiver comprises a sampling module 510 for sampling the signalreceived in a base band at the rate Nf where N is the number ofsub-carriers and f is the frequency of the FBMC symbols. The samples aregrouped together in the form of blocks of size N by a serial-parallelconverter 520.

Each block is filtered by a transmultiplexer made up of a battery of Npolyphase filters (PPN), 530, then undergoes an FFT of size N, in theFFT module 540, which operates on the N outputs from these filters.

The receiver is assumed to be synchronised on the FBMC symbols, in otherwords the start of an FFT window coincides with the first sample of anFBMC symbol (transmitted by one or the other of the transmissionantennae). Moreover the receiver is assumed to be synchronised on theinstants of use of the channel so that it knows the instants ofreception of the first and second blocks.

A demultiplexer 550 supplies the vectors at the output from the FFT at afirst output 551 during the first use of the channel and at a secondoutput 552 during the second use of the channel. The L vectors (of sizeN) generated sequentially at the first output are stored in a firstbuffer memory 561, configured in the form of a FIFO (first-in first-out)buffer. The L vectors generated sequentially at the second output arealso stored in a second buffer memory 562 configured in the form of aLIFO (last-in first-out) buffer. The conjugation module 570 thus readsthe L vectors in the reverse order to that in which they are stored, soas to perform a time-reversal, and carries out a complex conjugation ofeach of these vectors.

Each element of a vector generated at the first output is multiplied in581 by the complex conjugate of the coefficient of the first elementarychannel between the first transmission antenna and the reception antennaat the frequency of the sub-carrier carrying the element in question(the operation is symbolised here by a multiplication of the vector atthe output from the buffer memory by the matrix H₀* defined below) andin 583 by the complex conjugate of the coefficient of the secondelementary channel between the second transmission antenna and thereception antenna at the same sub-carrier frequency (the operation issymbolised here by a multiplication of the vector of samples at the FFToutput by the matrix H₁*). The matrices H₀ and H₁ are here understood tobe of size N×N and here represent the coefficients of the elementarychannels for the N sub-carriers. The matrices H₀ and H₁ are diagonal. Itis assumed that the matrices H₀ and H₁ are constant over the duration ofthe sequence (flat fading over time is assumed).

Similarly, each element of a vector generated at the second output ismultiplied in 582 by the coefficient of the channel between the firsttransmission antenna and the reception antenna at the frequency of thesub-carrier carrying the element in question (operation symbolised by amultiplication of the vector at the output of the FFT by the matrix H₀)and in 584 by the coefficient of the channel between the secondtransmission antenna and the reception antenna at the frequency of thesame sub-carrier (operation symbolised by a multiplication of the vectorat the output of the FFT by the matrix H₁).

The vectors at the output of the multiplier 581 are summed, element byelement, with those at the output of the multiplier 584 in the summer591. The successive vectors at the output of the summer 591 are thensupplied to a first OQAM demodulator (not shown).

Similarly the vectors at the output of the multiplier 583 aresubtracted, element by element, from those at the output of themultiplier 582, in the summer 592. The successive vectors at the outputof the summer 592 are then supplied to a second OQAM demodulator (notshown).

In other words, if Y ₀ and Y ₁ represent the matrices of size N×L whichrepresent the sequence of L column vectors at the output from the FFT,during the first and second use of the channel respectively, theestimates of the vectors of symbols X ₀ and X ₁ are obtained by:

$\begin{matrix}{{\hat{\overset{\_}{X}}}_{0} = {\frac{1}{{Tr}( {{H_{0}^{*}H_{0}} + {H_{1}^{*}H_{1}}} )}( {{H_{0}^{*}{\overset{\_}{Y}}_{0}} + {H_{1}{\overset{\_}{Y}}_{1}^{*}T}} )}} & ( {7\text{-}1} ) \\{{\hat{\overset{\_}{X}}}_{1} = {\frac{1}{{Tr}( {{H_{0}^{*}H_{0}} + {H_{1}^{*}H_{1}}} )}( {{H_{1}^{*}{\overset{\_}{Y}}_{0}} - {H_{0}{\overset{\_}{Y}}_{1}^{*}T}} )}} & ( {7\text{-}2} )\end{matrix}$

The reception method described above works for an FBMC receiverimplemented using a battery of polyphase filters. It is not applicableto an FS-FBMC receiver as described in relation to the right handportion of FIG. 1, given that the filtering is then carried outdownstream of the FFT.

The purpose of the present invention is consequently to offer a methodof reception of a sequence of blocks of FBMC symbols coded using blockAlamouti coding, which functions for an FS-FBMC receiver. The presentinvention also relates to an FS FBMC receiver capable of implementingthis method of reception.

DESCRIPTION OF THE INVENTION

The present invention is defined by a method for reception of signalstransmitted by a FBMC transmitter using block Alamouti coding, where theFBMC transmitter uses a plurality N of sub-carriers and an overlapfactor K of prototype filters, where the signal received by the receiveris translated to a base band, sampled at a frequency Nf where f is thehalf-frequency of the FBMC symbols, then undergoes a sliding FFT of sizeKN to provide sample vectors, wherein said sample vectors are receivedon a first path during a first channel use and on a second path during asecond channel use, the channel comprising a first elementary channelbetween a first antenna of the transmitter and a first antennae of thereceiver and a second elementary channel between a second antenna of thetransmitter and a second antenna of the receiver, said first and secondelementary channels being characterised, respectively, by a first and asecond transfer matrix (H₀,H₁), each vector (W₀ ^(m)) in a sequence ofvectors received on the first path being multiplied by the conjugate ofthe first transfer matrix in order to provide a first vector and by theconjugate of the second transfer matrix in order to provide a secondvector, where a sequence of vectors received on the second path istime-reversed and each vector (W₁ ^(L−1−m)) of the second sequence isconjugated before being multiplied by the first transfer matrix toprovide a third vector and by the second transfer matrix to provide afourth vector, where the first and fourth vectors are combined toprovide a first combined vector, the second and third vectors arecombined to provide a second combined vector, where the first and secondcombined vectors are spectrally de-spread and filtered in the frequencydomain by the prototype filters in order to provide, respectively, anestimate of a first data vector ({circumflex over (X)}₀ ^(m))transmitted via the first antenna of the transmitter and a second datavector ({circumflex over (X)}₁ ^(m)) transmitted via the secondtransmitter antenna.

According to a first alternative, the first and second antennas of thereceiver form a single antenna, and said sample vectors aredemultiplexed on the first path during the first use of the channel andon the second path during the second use of the channel.

According to a second alternative, the first and second antennas aredistinct, with the first path being associated with the first antenna ofthe receiver and the second path being associated with the secondantenna of the receiver.

Advantageously, if the transmitter uses the following matrix as a blockAlamouti coding matrix:

$\overset{\_}{C} = \begin{pmatrix}{\overset{\_}{X}}_{0} & {\overset{\_}{X}}_{1} \\{{- {\overset{\_}{X}}_{1}}T} & {{\overset{\_}{X}}_{0}T}\end{pmatrix}$where X ₀ and X ₁ are first and second blocks of input data vectorstransmitted during the first use of the channel via the first antennaand the second antenna of the receiver respectively, X ₁T is a firsttransformed block obtained by time-reversal and of the second block, X₀T is a second transformed block obtained by time-reversal of the firstblock, where the blocks −X ₁T and X ₀T are transmitted during the seconduse of the channel via the first antenna and the second antenna of thetransmitter respectively, according to a first embodiment, the vectorsof the second sequence are multiplied by a factor (j^(L−1)) where L isthe size of the first and second blocks of input data vectors, afterconjugation and before multiplication by the first and second transfermatrices.

In this case the input data vector of rank m in the first block of inputdata vectors, X₀ ^(m), and the input data vector of rank m in the secondblock of input data vectors, X₁ ^(m), may then be estimated from:{circumflex over (X)} ₀ ^(m) =μG(H ₀ *W ₀ ^(m) +j ^(L−1) H ₁ W ₁^(L−1−m)*)⊙M ^(m)*{circumflex over (X)} ₁ ^(m) =μG(H ₁ *W ₀ ^(m) −j ^(L−1) H ₀ W ₁^(L−1−m)*)⊙M ^(m)*where {circumflex over (X)}₀ ^(m) and {circumflex over (X)}₁ ^(m) arerespectively the estimates of the vectors X₀ ^(m) and X₁ ^(m), H₀, H₁are respectively the first and second transfer matrices, W₀ ^(m) thevector of rank m received on the first path, W₁ ^(L−1−m) the vector ofrank L−1−m received on the second path, M^(m) a vector which representsan OQAM coding of vectors X₀ ^(m) and X₁ ^(m), G a matrix whichrepresents, in the frequency domain, a spectral de-spreading andfiltering by prototype filters, μ is a coefficient of normalisation and⊙ represents the Hadamard product.

Alternatively, if the transmitter uses this matrix as a block Alamouticoding matrix:

${\overset{\_}{C}}^{\prime} = \begin{pmatrix}{\overset{\_}{X}}_{0} & {\overset{\_}{X}}_{1} \\{{- ( j^{L - 1} )}{\overset{\_}{X}}_{1}T} & {( j^{L - 1} ){\overset{\_}{X}}_{0}T}\end{pmatrix}$where X ₀ and X ₁ are the first and second blocks of input data vectorstransmitted during the first use of the channel, via the first antennaand the second antenna respectively of the transmitter, X ₁T is a firsttransformed block obtained by time-reversal and of the second block, X₀T is a second transformed block obtained by time reversal of the firstblock, according to a second embodiment of the invention, the vectors ofthe second sequence, after conjugation, are multiplied directly by thefirst and second transfer matrices.

In this case the input data vector of rank m in the first block of inputdata vectors, X₀ ^(m), and the input data vector of rank m in the secondblock of input data vectors, X₁ ^(m), are estimated from:{circumflex over (X)} ₀ ^(m) =μG(H ₀ *W ₀ ^(m) +H ₁ W ₁ ^(L−1−m)*)⊙M^(m)*{circumflex over (X)} ₁ ^(m) =μG(H ₁ *W ₀ ^(m) −H ₁ W ₁ ^(L−1−m)*)⊙M^(m)*where {circumflex over (X)}₀ ^(m) and {circumflex over (X)}₁ ^(m) arerespectively the estimates of the vectors X₀ ^(m) and X₁ ^(m), H₀, H₁are respectively the first and second transfer matrices, W₀ ^(m) thevector of rank m received on the first path, W₁ ^(L−1−m) the vector ofrank L−1−m received on the second path, M^(m) a vector which representsan OQAM coding of vectors X₀ ^(m) and X₁ ^(m), G a matrix whichrepresents, in the frequency domain, a spectral de-spreading andfiltering by prototype filters, μ is a coefficient of normalisation and⊙ represents the Hadamard product.

In both the preceding cases the first and second blocks of input datavectors may be preceded, respectively, by a first and by a secondpreamble, with a first guard block made up of null vectors separatingthe first block of data vectors and the first transformed block, with asecond guard block made up of null vectors separating the second blockof data vectors and the second transformed block. Since the first andsecond preambles are known to the receiver, then advantageously on thefirst path, at the output of the sliding FFT, an elimination of theinterference affecting the vectors received on the first path isperformed by subtraction from this path of the contribution due to thefirst and second preambles.

BRIEF DESCRIPTION OF THE ILLUSTRATIONS

Other characteristics and advantages of the invention will appear onreading the preferential embodiments of the invention made in referenceto the attached figures, among which:

FIG. 1 schematically shows a FS-FBMC telecommunication system known tothe prior art;

FIG. 2A shows the spectral spreading undertaken upstream of the IFFTmodule of FIG. 1;

FIG. 2B shows the spectral de-spreading undertaken downstream of theIFFT module of FIG. 1;

FIG. 3 shows the combination of FBMC symbols in FIG. 1;

FIG. 4 schematically shows the transmission of two sequences of blocksof symbols by an FBMC transmitter using a block Alamouti coding known inthe prior art;

FIG. 5 schematically shows the architecture of an FBMC receiver used toreceive sequences of blocks of symbols transmitted by the transmitter inFIG. 4;

FIG. 6 schematically shows the architecture of an FS-FBMC receiver,according to a first embodiment of the invention, used to receivesequences of blocks of symbols coded by a block Alamouti coding;

FIG. 7 schematically shows the architecture of a FS-FBMC receiveraccording to one alternative of the first embodiment of the invention.

FIG. 8A schematically shows a first example of transmission of twosequences of blocks of symbols by an FBMC transmitter using a firstblock Alamouti coding;

FIG. 8B schematically shows a second example of transmission of twosequences of blocks of symbols by an FBMC transmitter using a secondblock Alamouti coding;

FIG. 9 schematically shows the architecture of an FS-FBMC receiver,according to a second embodiment of the invention, used to receivesequences of blocks transmitted according to the schematicrepresentation in FIG. 8B.

DETAILED DESCRIPTION OF PARTICULAR EMBODIMENTS

In order to facilitate understanding of the notations, we will first ofall consider an FS-FBMC transmitter as described in relation to FIG. 1.

Unlike preceding notations, the column vectors X^(m), m=0, . . . , L−1,of size N, will, in what follows, represent the input data vectors, inother words the data at the input to the OQAM modulator. The elements ofthese vectors are therefore real value elements.

The signal transmitted by the transmitter at the instant m can berepresented by a column vector Z^(m) of size KN whose elements aresamples at a frequency Nf. The vector Z^(m) can be expressed as afunction of the input data vectors X^(m−(K−1)), . . . , X^(m), . . . ,X^(m+(K−1)), that is:

$\begin{matrix}{Z^{m} = {{F^{H}{G( {X^{m} \odot M^{m}} )}} + {\sum\limits_{p = 1}^{K - 1}\;{Q_{\frac{pN}{2}}F^{H}{G( {X^{m - p} \odot M^{m - p}} )}}} + {Q_{{KN} - \frac{pN}{2}}F^{H}{G( {X^{m + p} \odot M^{m + p}} )}}}} & (8)\end{matrix}$where ⊙ is the Hadamard product, F is the discrete Fourier transformmatrix of size KN×KN, G is a matrix of size KN×N representing thespectral spreading and the transfer function of the prototype filter inthe frequency domain, that is:

$\begin{matrix}{G = \begin{pmatrix}G_{K - 1} & 0 & \cdots & 0 \\\vdots & G_{K - 1} & \ddots & \vdots \\G_{0} & \vdots & \ddots & 0 \\\vdots & G_{0} & \ddots & G_{K - 1} \\G_{{- K} + 1} & \vdots & \ddots & \vdots \\0 & G_{{- K} + 1} & \ddots & G_{0} \\\vdots & \ddots & \ddots & \vdots \\0 & \cdots & 0 & G_{{- K} + 1}\end{pmatrix}} & (9)\end{matrix}$M^(m) is a column vector of size N which expresses the OQAM modulation,namely a vector whose elements are given by:M ^(m) [k]=j ^(m+k)(−1)^(km)  (10)and Q_(l) is an offset matrix of l samples, of size KN×KN defined by:

$\begin{matrix}{Q_{l} = \begin{pmatrix}0_{l \times {({{KN} - l})}} & 0_{l \times l} \\I_{{KN} - l} & 0_{{({{KN} - l})} \times l}\end{pmatrix}} & (11)\end{matrix}$where T_(KN−)

is the identity matrix of size (KN−l)×(KN−

)

It will be understood that the terms beneath the summation sign inexpression (8) represent the 2K−1 FBMC symbols which are combined inFIG. 3.

The signal received by the FBMC receiver at the instant in may similarlybe expressed in the form of a data vector at the output of the OQAMdemodulator, here referred to as Y^(m), of size KN. The vector Y^(m) canbe expressed as a function of the vector Z^(m) which represents thetransmitted signal, either by carrying out abstraction of the noiseterm:Y ^(m)=(G ^(H) FH ₀ Z ^(m))⊙M ^(m)*  (12)or, given that G^(H)FF^(H)G=I_(N) and that (X^(m) ⊙M^(m))⊙M^(m)*=X^(m):

$\begin{matrix}{{Y^{m} = {H_{0}( {X^{m} + {\sum\limits_{p = 1}^{K - 1}\;{{U^{p}( {X^{m - p} \odot M^{m - p}} )} \odot M^{m^{*}}}} + {\sum\limits_{p = 1}^{K - 1}\;{{V^{p}( {X^{m + p} \odot M^{m + p}} )} \odot M^{m^{*}}}}} )}}\text{where:}} & (13) \\{U^{p} = {{G^{H}{FQ}^{\frac{pN}{2}}F^{H}G\mspace{14mu}{and}\mspace{14mu} V^{p}} = {G^{H}{FQ}^{{KN} - \frac{pN}{2}}F^{H}G}}} & (14)\end{matrix}$

It will be seen that G^(H)=G^(T) given that the coefficients of thefilter transfer matrix are real.

It is now assumed that a block Alamouti coding is carried out, with acoding matrix defined by:

$\begin{matrix}{\overset{\_}{C} = \begin{pmatrix}{\overset{\_}{X}}_{0} & {\overset{\_}{X}}_{1} \\{{- {\overset{\_}{X}}_{1}}T} & {{\overset{\_}{X}}_{0}T}\end{pmatrix}} & (15)\end{matrix}$

The basic idea of the invention is to use a receiver implemented in thefrequency domain (FS-FBMC receiver) and to combine the two blocks at theoutput of the FFT module (module 170 in FIG. 1), during the first andsecond use of the channel respectively.

Then X₀ ^(m) is the m^(th) input data vector of the first block X ₀ andX₁ ^(m) the m^(th) input data vector of the second block X ₁respectively. Furthermore W₀ ^(m) is the m^(th) sample vector at theoutput to the FFT module, before de-spreading and filtering, during thefirst use of the channel. Similarly, W₁ ^(m) is the m^(th) sample vectorat the output of the FFT module, before de-spreading and filtering,during the second use of the channel.

During the first use of the channel the vector W₀ ^(m) can be expressedas follows:

$\begin{matrix}{W_{0}^{m} = {{H_{0}( {{G( {X_{0}^{m} \odot M^{m}} )} + {\sum\limits_{p = 1}^{K - 1}\;{A^{p}( {X_{0}^{m - p} \odot M^{m - p}} )}} + {\sum\limits_{p = 1}^{K - 1}\;{B^{p}( {X_{0}^{m + p} \odot M^{m + p}} )}}} )} + {H_{1}( {{G( {X_{1}^{m} \odot M^{m}} )} + {\sum\limits_{p = 1}^{K - 1}\;{A^{p}( {X_{1}^{m - p} \odot M^{m - p}} )}} + {\sum\limits_{p = 1}^{K - 1}\;{B^{p}( {X_{1}^{m + p} \odot M^{m + p}} )}}} )}}} & (16) \\{{{where}\mspace{14mu} A^{p}} = {{{FQ}^{\frac{pN}{2}}F^{H}\mspace{14mu}{and}\mspace{14mu} B^{p}} = {{FQ}^{{KN} - \frac{pN}{2}}{F^{H}.}}}} & (17)\end{matrix}$

Similarly, during the second use of the channel the vector W₁ ^(m) canbe expressed as follows:

$\begin{matrix}{W_{1}^{m} = {{- {H_{0}( {{G( {X_{1}^{L - 1 - m} \odot M^{m}} )} + {\sum\limits_{p = 1}^{K - 1}\;{A^{p}( {X_{1}^{L - 1 - m + p} \odot M^{m - p}} )}} + {\sum\limits_{p = 1}^{K - 1}\;{B^{p}( {X_{1}^{L - 1 - m - p} \odot M^{m + p}} )}}} )}} + {H_{1}( {{G( {X_{0}^{L - 1 - m} \odot M^{m}} )} + {\sum\limits_{p = 1}^{K - 1}\;{A^{p}( {X_{0}^{L - 1 - m + p} \odot M^{m - p}} )}} + {\sum\limits_{p = 1}^{K - 1}\;{B^{p}( {X_{0}^{L - 1 - m - p} \odot M^{m + p}} )}}} )}}} & (18)\end{matrix}$an expression in which good use has been made of the fact that the inputdata vectors were real value vectors.It will be seen that the transfer matrices for the elementary channels,H₀ and H₁ are here of size KN×KN due to the spectral spreading.

If the block of vectors W₁ ^(m), m=0, . . . , L−1, is transformed bytime-reversal and complex conjugation of the block, the m^(th) vector ofthe block transformed in this way may be written, from (18):

$\begin{matrix}{W_{1}^{L - m - 1^{*}} = {{- {H_{0}^{*}( {{G( {X_{1}^{m} \odot M^{L - 1 - m^{*}}} )} + {\sum\limits_{p = 1}^{K - 1}\;{A^{p^{*}}( {X_{1}^{m + p} \odot M^{L - 1 - m - p^{*}}} )}} + {\sum\limits_{p = 1}^{K - 1}\;{B^{p^{*}}( {X_{1}^{m - p} \odot M^{L - 1 - m + p^{*}}} )}}} )}} + {H_{1}^{*}( {{G( {X_{0}^{m} \odot M^{L - 1 - m^{*}}} )} + {\sum\limits_{p = 1}^{K - 1}\;{A^{p^{*}}( {X_{0}^{m + p} \odot M^{L - 1 - m - p^{*}}} )}} + {\sum\limits_{p = 1}^{K - 1}\;{B^{p^{*}}( {X_{0}^{m - p} \odot M^{L - 1 - m + p^{*}}} )}}} )}}} & (19)\end{matrix}$That is by taking into consideration that:M ^(L−1−m) *=−M ^(m) j ^(L−1) ; M ^(L−1−m-p) *=−M ^(m+p) j ^(L−1) ; M^(L−1−m+p) *=−M ^(m−p) j ^(L−1)where it is assumed that the size L of the block was an even number, andthat:A ^(p) *=B ^(p) ; B ^(p) *=A ^(p)the vector W₁ ^(L−m−1)* of the reversed block can finally be written as:

$\begin{matrix}{W_{1}^{L - m - 1^{*}} = {{H_{0}^{*}{j^{L - 1}( {{G( {X_{1}^{m} \odot M^{m}} )} + {\sum\limits_{p = 1}^{K - 1}\;{B^{p}( {X_{1}^{m + p} \odot M^{m + p}} )}} + {\sum\limits_{p = 1}^{K - 1}\;{A^{p}( {X_{1}^{m - p} \odot M^{m - p}} )}}} )}} - {H_{1}^{*}{j^{L - 1}( {{G( {X_{0}^{m} \odot M^{m}} )} + {\sum\limits_{p = 1}^{K - 1}\;{B^{p}( {X_{0}^{m + p} \odot M^{m + p}} )}} + {\sum\limits_{p = 1}^{K - 1}\;{B^{p}( {X_{0}^{m - p} \odot M^{m - p}} )}}} )}}}} & (20)\end{matrix}$

The vectors of the transmitted data X₀ ^(m), X₁ ^(m) can be estimated byundertaking a combination of vectors W₀ ^(m) and W₁ ^(L−m−1)*{hacek over (X)} ₀ ^(m)=μ(H ₀ *W ₀ ^(m) +j ^(L−1) H ₁ W ₁^(L−1−m)*)  (21-1){hacek over (X)} ₁ ^(m)=μ(H ₁ *W ₀ ^(m) −j ^(L−1) H ₀ W ₁^(L−1−m)*)  (21-2)where

${\mu = \frac{1}{{Tr}( {{H_{0}^{H}H_{0}} + {H_{1}^{H}H_{1}}} )}},$then filtering and spectral de-spreading and finally an OQAMdemodulation:{circumflex over (X)} ₀ ^(m) =μG(H ₀ *W ₀ ^(m) +j ^(L−1) H ₁ W ₁^(L−1−m)*)⊙M ^(m)*  (22-1){circumflex over (X)} ₁ ^(m) =μG(H ₁ *W ₀ ^(m) −j ^(L−1) H ₀ W ₁^(L−1−m)*)⊙M ^(m)*  (22-2)

FIG. 6 schematically shows the architecture of an FS-FBMC receiver,according to a first embodiment of the invention, used to receivesequences of blocks of symbols coded by a block Alamouti coding.

The receiver comprises a sampling module 610 for sampling the signalreceived in a base band at the rate of Nf where N is the number ofsub-carriers and f is the frequency of the FBMC symbols. The samples aregrouped together in the form of blocks of size KN by a serial-parallelconverter 620.

The receiver is assumed to be synchronised on the FBMC symbols, in otherwords, the start of an FFT window coincides with the first sample of anFBMC symbol (transmitted by one or the other of the transmissionantennae). Moreover, the receiver is assumed to be synchronised on theinstants of use of the channel so that it knows the instants at whichthe first and second blocks are received.

The blocks of samples undergo a FFT of size KN in the FFT module 630.

A demultiplexer 640 supplies the vectors at the output from the FFT at afirst output 641 during the first use of the channel and at a secondoutput 642 during the second use of the channel. The L vectors (of sizeKN) generated sequentially at the first output are stored in a firstbuffer memory 651, configured in the form of a FIFO (first-in first-out)buffer. The L vectors generated sequentially at the second output arealso stored in a second buffer memory 652 configured in the form of aLIFO (last-in first-out) buffer. The module 660 thus reads the L vectorsin the reverse order to that in which they are stored (LIFO), so as toperform a time-reversal and furthermore undertakes a complex conjugationof each of these vectors. A multiplier 670 multiplies the elements ofthe vectors at the output from the module 660 by (j)^(L−1), in otherwords by j if L is an even number.

Each element of a vector generated at the first output is multiplied in681 by the complex conjugate of the coefficient of the first elementarychannel between the first transmission antenna and the receptionantenna, at the frequency of the sub-carrier carrying the element inquestion (the operation is symbolised here by a multiplication of thevector at the output from the buffer memory by the matrix H₀*) and in683 by the complex conjugate of the coefficient of the second elementarychannel between the second transmission antenna and the receptionantenna, at the same sub-carrier frequency (the operation is symbolisedhere by a multiplication of the vector of samples at the FFT output bythe matrix H₁*). The matrices H₀ and H₁ are here meant to be of sizeKN×KN and here represent the coefficients of the elementary channels forthe KN spectrally spread sub-carriers. An identical channel coefficientcan be chosen for the K frequencies produced by a given sub-channel. Itis assumed that the matrices H₀ and H₁ are constant over the duration ofthe sequence (flat fading assumption).

Similarly, each element in a vector generated at the second output ismultiplied in 682 by the coefficient for the channel between the firsttransmission antenna and the reception antenna at the frequency of thesub-carrier carrying the element in question (operation symbolised by amultiplication of the vector at the output of the FFT by the matrix H₀)and in 684 by the coefficient of the channel between the secondtransmission antenna and the reception antenna at the frequency of thesame sub-carrier (operation symbolised by a multiplication of the vectorat the output of the FFT by the matrix H₁).

The vectors at the output of the multiplier 681 are summed, element byelement, with those at the output of the multiplier 684, in the summer691. The successive vectors of size N at the output of the summer 691are then supplied to a first spectral de-spreading and filtering module695.

Similarly, the vectors at the output of the multiplier 682 aresubtracted, element by element, from those at the output of themultiplier 683, in the summer 692. The successive vectors of size N atthe output of the summer 692 are then supplied to a second spectralde-spreading and filtering module 696.

The vectors obtained by the first and second modules 695 and 696 thenundergo OQAM demodulation (not shown) in order to obtain the estimateddata vectors {circumflex over (X)}₀ ^(m) and {circumflex over (X)}₁^(m), m=0, . . . , L−1.

FIG. 7 schematically shows the architecture of a FS-FBMC receiveraccording to one alternative of the first embodiment of the invention.

Unlike the FS-FBMC receiver of FIG. 6, the receiver here comprises tworeception antennas. The signal received on the first antenna during thefirst use of the channel is demodulated into a base band then sampled ata rate Nf in the sampler 711. The samples are grouped together in theform of blocks of size KN by the serial-parallel converter 721 beforeundergoing a sliding FFT of size KN in 731. The vectors of the samplesat the output of the FFT are then processed on a first path.

Similarly the signal received on the second antenna during the seconduse of the channel is demodulated into a base band then sampled at arate Nf in the sampler 712. The samples are grouped together in the formof blocks of size KN by the serial-parallel converter 722 beforeundergoing a sliding FFT of size KN in 732. The vectors of the samplesat the output of the FFT are then processed on a second path.

The remaining elements 751-796 are, respectively, identical to elements651-696 of FIG. 6.

It will be understood that unlike the FS-FBMC receiver in FIG. 6, nodemultiplexing is carried out at the FFT output since both paths areseparated from the reception antennas. It is necessary, however, thatthe receiver be synchronised with the FBMC symbol and, moreover, thatthe first path be synchronised with the instants of the first use of thechannel and that the second path be synchronised with the instants ofsecond use of the channel.

The structure of the receiver of FIG. 6 or of FIG. 7 can be simplifiedwhen the transmitter, instead of using the coding given by (15), usesthe block Alamouti coding defined by:

$\begin{matrix}{{\overset{\_}{C}}^{\prime} = \begin{pmatrix}{\overset{\_}{X}}_{0} & {\overset{\_}{X}}_{1} \\{{- ( j^{L - 1} )}{\overset{\_}{X}}_{1}T} & {( j^{L - 1} ){\overset{\_}{X}}_{0}T}\end{pmatrix}} & (23)\end{matrix}$

In this case the multiplication by the factor (j^(L−1)) can be removedat the reception and consequently the multiplier 670 or 770 can beomitted.

FIG. 8A schematically shows a first example of the transmission of twosequences of blocks of symbols by an FBMC transmitter using a firstblock Alamouti coding, as given by the coding matrix given by theexpression (15).

The blocks of data to be transmitted are here considered upstream of theOQAM modulation.

A first sequence of blocks 801 is formed by a first guard block 811, afirst block of L input data vectors, X ₀, 821, a second guard block,831, followed by a first transformed block, −X ₁T, 841, obtained bytime-reversal and change of sign of the first input data block.

A second sequence of blocks 802 is formed by a first guard block 812, asecond block of L input data vectors, X ₁, 822, a second guard block,832, followed by a second transformed block, X ₀T, 842, obtained bytime-reversal and change of sign of the first input data block.

The guard blocks are made up of null vectors in order to preventinterference between the data blocks and the transformed blocks.

The first and second sequences are respectively transmitted by the firstand second antennas, 892 and 892, after FBMC modulation.

FIG. 8B schematically shows a second example of the transmission of twosequences of blocks of symbols by an FBMC transmitter using a secondblock Alamouti coding.

The second example is identical to the first except that the first guardblock is replaced in the first sequence by a first preamble 811′ and inthe second by sequence by a second preamble 812′. The other blocksremain unchanged and are therefore not described again.

The first and second preambles generate interference which affects thefirst symbols of the blocks X ₀ and X ₁, interference which does notsymmetrically affect the blocks −X ₁T and X ₀T. This asymmetry does notallow the interference for the input data vectors X₀ ^(m), X₁ ^(m) atthe beginning of the block, to be eliminated. The preamble symbols arehowever known to the receiver and it is possible to eliminate thisinterference once an estimate of the transmission channel is available.

FIG. 9 schematically shows the architecture of an FS-FBMC receiver,according to a second embodiment of the invention, used to receivesequences of blocks in FIG. 8B.

Apart from the interference canceller 945, the elements 910 to 996 areidentical to the elements 610 to 696 already described in relation toFIG. 6.

The interference canceller 945 is located on the first output from thedemultiplexer 940 and therefore only operates during the first use ofthe channel. Its purpose is to eliminate the interference generated atthe receiver by the first and second preambles 811′ and 812′, on thepayload X ₀, X ₁. More precisely, the interference canceller receives anestimate of the transmission channel, namely the transfer matrices forthe elementary channels H₀ and H₁. Since the preambles 811′ and 812′ areknown to the receiver, the latter can reconstitute the contribution ofthe preambles to the signal received during the reception of blocks X_(o) and X ₁, it being understood that only the first K+E vectorsreceived at the beginning of these blocks are affected by thisinterference, where K is the length of the prototype filter and E thetime-spreading of the channel expressing as number of samples. Thecontribution of the preambles is subtracted from the received signal atthe output of the FFT module 830. Once the interference is eliminated,the transmitted blocks X ₀ and X ₁ may be estimated in accordance with(22-1) and (22-1), it being understood once more that the term j^(L−1)may be omitted if the block Alamouti coding defined by (23) is used.Those skilled in the art will moreover understand that this secondembodiment may also take the form of the alternative in FIG. 7 by addingan interference canceller at the output of the FFT module 731.

The invention claimed is:
 1. A method comprising: receiving, by areceiver, signals transmitted by an FBMC transmitter using blockAlamouti coding, where the FBMC transmitter uses a plurality N ofsub-carriers and an overlap factor K of prototype filters; translatingthe signal received by the receiver to a base band, sampled at afrequency Nf where f is the half-frequency of the FBMC symbols; thenperforming a sliding FFT of size KN on the signal to provide samplevectors, wherein said sample vectors are received on a first path duringa first channel use and on a second path during a second channel use,the channel comprising a first elementary channel between a firstantenna of the transmitter and a first antenna of the receiver and asecond elementary channel between a second antenna of the transmitterand a second antenna of the receiver, said first and second elementarychannels being characterized, respectively, by a first and a secondtransfer matrix (H₀, H₁); multiplying each vector (W₀ ^(m)) in asequence of vectors received on the first path by the conjugate of thefirst transfer matrix in order to provide a first vector and by theconjugate of the second transfer matrix in order to provide a secondvector; time-reversing a sequence of vectors received on the second pathand conjugating each vector (W₁ ^(L−1−m)) of the second sequence beforemultiplying each vector (W₁ ^(L−1−m)) of the second sequence by thefirst transfer matrix to provide a third vector and by the secondtransfer matrix to provide a fourth vector; and combining the first andfourth vectors to provide a first combined vector, the second and thirdvectors being combined to provide a second combined vector, where thefirst and second combined vectors are spatially de-spread and filteredin the frequency domain by the prototype filters to provide,respectively, an estimate of a first data vector ({circumflex over (X)}₀^(m)) transmitted via the first antenna of the transmitter and of asecond data vector ({circumflex over (X)}₁ ^(m)) transmitted via thesecond transmitter antenna.
 2. The method according to claim 1, whereinthe first and second antennas of the receiver form a single antenna, andin that said sample vectors are demultiplexed on the first path duringthe first use of the channel and on the second path during the seconduse of the channel.
 3. The method of according to claim 1, wherein thefirst and second antennas are distinct, with the first path beingassociated with the first antenna of the receiver and the second pathbeing associated with the second antenna of the receiver.
 4. The methodof according to claim 1, where the transmitter uses the following matrixas a matrix for block Alamouti coding:$\overset{\_}{C} = \begin{pmatrix}{\overset{\_}{X}}_{0} & {\overset{\_}{X}}_{1} \\{{- {\overset{\_}{X}}_{1}}T} & {{\overset{\_}{X}}_{0}T}\end{pmatrix}$ where X ₀ and X ₁ are first and second blocks of inputdata vectors transmitted during the first use of the channel via thefirst antenna and the second antenna of the receiver respectively, X ₁Tis a first transformed block obtained by time-reversal and of the secondblock, X ₀T is a second transformed block obtained by time-reversal ofthe first block, where the blocks −X ₁T and X ₀T are transmitted duringthe second use of the channel via the first antenna and the secondantenna of the transmitter respectively, wherein the vectors of thesecond sequence are multiplied by a factor (j^(L−1)) where L is the sizeof the first and second blocks of input data vectors, after conjugationand before multiplication by the first and second transfer matrices. 5.The method according to claim 4, wherein the input data vector of rank min the first block of input data vectors, X₀ ^(m), and the input datavector of rank m in the second block of input data vectors, X₁ ^(m), areestimated from:{circumflex over (X)} ₀ ^(m) =μG(H ₀ *W ₀ ^(m) +j ^(L−1) H ₁ W ₁^(L−1−m)*)⊙M ^(m)*{circumflex over (X)} ₁ ^(m) =μG(H ₁ *W ₀ ^(m) −j ^(L−1) H ₀ W ₁^(L−1−m)*)⊙M ^(m)* where {circumflex over (X)}₀ ^(m) and {circumflexover (X)}₁ ^(m) are respectively the estimates of the vectors X₀ ^(m)and X₁ ^(m), H₀, H₁ are respectively the first and second transfermatrices, W₀ ^(m) the vector of rank m received on the first path, W₁^(L−1−m) the vector of rank L−1−m received on the second path, M^(m) avector which represents a OQAM coding of vectors X₀ ^(m) and X₁ ^(m), Ga matrix which represents, in the frequency domain, a spectralde-spreading and filtering by prototype filters, μ is a coefficient ofnormalisation and ⊙ represents the Hadamard product.
 6. The methodaccording to claim 1, wherein the transmitter uses the following matrixas a matrix for block Alamouti coding:${\overset{\_}{C}}^{\prime} = \begin{pmatrix}{\overset{\_}{X}}_{0} & {\overset{\_}{X}}_{1} \\{{- ( j^{L - 1} )}{\overset{\_}{X}}_{1}T} & {( j^{L - 1} ){\overset{\_}{X}}_{0}T}\end{pmatrix}$ where X ₀ and X ₁ are the first and second blocks ofinput data vectors transmitted during the first use of the channel viathe first antenna and the second antenna, respectively, of thetransmitter, X ₁T is a first transformed block obtained by time-reversaland of the second block, X ₀T is a second transformed block obtained bytime reversal of the first block, wherein the vectors of the secondsequence, after conjugation, are multiplied directly by the first andsecond transfer matrices.
 7. The method according to claim 6, whereinthe input data vector of rank m in the first block of input datavectors, X₀ ^(m), and the input data vector of rank m in the secondblock of input data vectors, X₁ ^(m), are estimated from:{circumflex over (X)} ₀ ^(m) =μG(H ₀ *W ₀ ^(m) +H ₁ W ₁ ^(L−1−m)*)⊙M^(m)*{circumflex over (X)} ₁ ^(m) =μG(H ₁ *W ₀ ^(m) −H ₁ W ₁ ^(L−1−m)*)⊙M^(m)* where {circumflex over (X)}₀ ^(m) and {circumflex over (X)}₁ ^(m)are respectively the estimates of the vectors X₀ ^(m) and X₁ ^(m), H₀,H₁ are respectively the first and second transfer matrices, W₀ ^(m) thevector of rank m received on the first path, W₁ ^(L−1−m) the vector ofrank L−1−m received on the second path, M^(m) a vector which representsa OQAM coding of vectors X₀ ^(m) and X₁ ^(m), G a matrix whichrepresents, in the frequency domain, a spectral de-spreading andfiltering by prototype filters, μ is a coefficient of normalisation and⊙ represents the Hadamard product.
 8. The method according to claim 4,where the first and second blocks of input data vectors are preceded,respectively, by first and second preambles, a first guard block made upof null vectors separating the first block of data vectors and the firsttransformed block, a second guard block made up of null vectorsseparating the second block of data vectors and the second transformedblock, wherein the first and second preambles are known to the receiverand that on the first path, at the output of the sliding FFT,elimination of the interference affecting the vectors received on thefirst path is carried out by subtraction at this path of thecontribution due to the first and second preambles.
 9. A receivercomprising: processing circuitry configured to receive signalstransmitted by an FBMC transmitter using block Alamouti coding, wherethe FBMC transmitter uses a plurality N of sub-carriers and an overlapfactor K of prototype filters, translate the signal received by thereceiver to a base band, sampled at a frequency Nf where f is thehalf-frequency of the FBMC symbols, perform a sliding FFT of size KN onthe signal to provide sample vectors, wherein said sample vectors arereceived on a first path during a first channel use and on a second pathduring a second channel use, the channel comprising a first elementarychannel between a first antenna of the transmitter and a first antennaof the receiver and a second elementary channel between a second antennaof the transmitter and a second antenna of the receiver, said first andsecond elementary channels being characterized, respectively, by a firstand a second transfer matrix (H₀, H₁), multiply each vector (W₀ ^(m)) ina sequence of vectors received on the first path by the conjugate of thefirst transfer matrix in order to provide a first vector and by theconjugate of the second transfer matrix in order to provide a secondvector, time-reverse a sequence of vectors received on the second pathand conjugating each vector (W₁ ^(L−1−m)) of the second sequence beforemultiplying each vector (W₁ ^(L−1−m)) of the second sequence by thefirst transfer matrix to provide a third vector and by the secondtransfer matrix to provide a fourth vector, and combine the first andfourth vectors to provide a first combined vector, the second and thirdvectors being combined to provide a second combined vector, where thefirst and second combined vectors are spatially de-spread and filteredin the frequency domain by the prototype filters to provide,respectively, an estimate of a first data vector ({circumflex over (X)}₀^(m)) transmitted via the first antenna of the transmitter and of asecond data vector ({circumflex over (X)}₁ ^(m)) transmitted via thesecond transmitter antenna.